New binary optimal LCD codes using heuristic embedding
Haeun Lim, Junmin An, Jon-Lark Kim
Abstract
In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found 14 optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.
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